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On a Fractional Master Equation

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  • Anitha Thomas

Abstract

A fractional order time-independent form of the wave equation or diffusion equation in two dimensions is obtained from the standard time-independent form of the wave equation or diffusion equation in two-dimensions by replacing the integer order partial derivatives by fractional Riesz-Feller derivative and Caputo derivative of order ð ›¼ , ð ›½ , 1 < â„œ ( ð ›¼ ) ≤ 2 and 1 < â„œ ( ð ›½ ) ≤ 2 respectively. In this paper, we derive an analytic solution for the fractional time-independent form of the wave equation or diffusion equation in two dimensions in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases, the solutions are represented also in terms of Fox's ð » -function.

Suggested Citation

  • Anitha Thomas, 2011. "On a Fractional Master Equation," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-13, October.
    • Handle: RePEc:hin:jnijde:346298
    DOI: 10.1155/2011/346298
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